Extruding faces are locked to a translation along a odd axis
One reason that things are looking strange is that you're editing with the SubSurf modifier turned on. I usually don't show the subsurf in edit mode, but there's nothing wrong with that.

The other thing that's making things act "strange" is that your "Pivot Point" is set to "Individual Origins," instead of "Median." To find that, look for a button that has two overlapping circles, and each circle has a blue dot in the center. It's between the "Display Mode" button and the "Show Manipulator" button. The "Display Mode" button has a wireframe sphere on it, and the "Show Manipulator" button looks like the three-axis manipulator that you see in the viewport.

Click on the "Pivot Point" button and choose the selection that has a single dot between both circles. This is "Median" and is the default. It will behave a bit more like you expect.

With "Individual Origins," it's trying to extrude each face along its own normal. you can find more information in the Blender Manual.